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I just graduated from high school (not as in, right just now, but this year) and while I love Math, I know its practical applications and everything, I'm confused as to how exactly it helps me become more intelligent.
In my country, India, people boast of how tough the JEE exam is (which is the entrance test for most of the colleges/universities in my country for Science/Engineering/Math, but not Medicine/Social Sciences/Arts/Commerce). One of the major reasons for the exam being touch is not only the fact that roughly 1.2 million people each year give the test in my country, but also because the test covers advanced topics in its subjects (Physics, Chemistry and Math).
Now, the thing that has disturbed me about not only this test, but standardized tests, in general (you can even take the example of SAT Math Level 2/1), is the fact that they don't really test your ability in the subject, but they test your fluency in taking that specific test. For example, my cousin brother is preparing for that test and he figured out the answer to one of the questions in the test by substituting the value of all the options given in the solution and I felt disgusted by it. How exactly does it improve your knowledge of Math and make you better at it? Even a 10 year old can substitute, add, multiply, divide and/or subtract to find the answer. How are you better than him/her?
Throughout high school, I observed that this observation (if I'm correct) is not valid of only standardized tests, but even what they taught me in school. No problem was exactly difficult. The only thing that differentiated an easy problem from a difficult one was the fact that the person solving the problem did not know the trick it required to solve the problem. Once you get to know that, you can very well repeat it like a machine for other similar problems to come, but with different numbers/variables.
Granted that using this way, I sometimes learned a little more Mathematics, and learned another technique of solving a problem, but is this really what Math is all about? Learning new tricks to solve problems? I'd be more excited about the same than I am if I were to come up with new techniques to solve problems. But the trend, at least in my country, is to know some trick of solving the problem, repeating it and getting better at it to spit it all out during the exam.
In school, Math has been about applying certain techniques to solve problems. But using this, do we really learn Math? Is this really what Math is all about? Learning tricks to solve problems?